Why a single SSD instead of the dual USB devices?
A single SSD is an order of magnitude faster and perhaps two orders of magnitude more reliable. If you read the forums, you'll see lots of people whining about boot/system issues... and the vast majority are running USB sticks. While cheap, USB sticks weren't really designed for that sort of service. And, these days, you can pick up cheap SSDs on eBay for not much. I bought a handful of Intel 320 40GB SSDs for $20-25/ea. I use them for boot devices for FreeNAS and my vSphere hosts. I have yet to have one fail. My most worn one (in my FreeNAS system) shows 11% on the media wear-out value.
We don't have any 4K cameras so 4K footage would only ever be worked on if we were given it by a client. How would you suggest getting the best performance out of the the 8 bays that are on the case that I have chosen? Would it be best if I upgraded to another case that has more drive bays?
Let's address this question first. Unfortunately, there's no one right answer... it all depends on your workload and your tolerance for slowness. There are people storing 4K video on a single-vdev, 6-disk pool. There are people on here building huge arrays using multiple drive racks. I would suggest starting with a single-vdev, 6-disk pool, configured in RAIDZ2. Get it running, see how it works for you. From there, you can decide if you want to add additional vdevs or if you need to consider moving to striped mirrors. You may also want to consider maximizing your RAM... unfortunately, RAM isn't cheap right now.
If you're seriously considering having multiple people working on 1080p or 4K video simultaneously from this system, I would at least consider a system with more expansion capabilities - both from a speed and a capacity perspective. Video has a way of growing quickly. If you can handle a rack-mounted system (space, noise), consider a system like I have in my signature. Mine is a 4U, 36-bay system. Lots of expansion capabilities. Many good deals for such systems may be found on eBay (just be careful and do your research before buying... you can get bit by things like SAS1 backplanes that won't handle drives over 2.2TB, etc.)
Would you suggest that I use 6 6TB drives instead since that would leave me with about 24TB of storage but cheaper than the 4 10TB drives? Also, why is it 15.74TB of usable storage and not an exact 16TB?
You should read up in the Resources section. One of the members put together a very good calculator, which you can find here:
https://jsfiddle.net/Biduleohm/paq5u7z5/1/embedded/result/
The size is based on the space consumed by metadata, the recommended maximum 80% usage, etc. 6x6TB drives would give you 18.89TB (that's 17.18TiB) usable. Assuming you opt for a system that supports more drives, yes, I think you'd be better served with 6x6TB drives.